4,2

Orthoplex polyominoes are multidimensional polyominoes that do not extend more than two units along any axis.

(B^2(x)+B(x^2))^2/8+B^2(x^2)/4+B(x^4)/4 +B^5(x)/(2-2B(x)) +B(x)B^2(x^2)/(2-2B(x^2)) where B(x) is generating function for rooted trees with n nodes

1 tetromino (a square) in 2^2 space; 2 pentominoes in 2^3 space;

in 2^4 space, 8 hexominoes that have cell centers determining 4-space

sb[ n_, k_ ] := sb[ n, k ]=b[ n+1-k, 1 ]+If[ n<2k, 0, sb[ n-k, k ] ]; b[ 1, 1 ] := 1;

b[ n_, 1 ] := b[ n, 1 ]=Sum[ b[ i, 1 ]sb[ n-1, i ]i, {i, 1, n-1} ]/(n-1);

b[ n_, k_ ] := b[ n, k ]=Sum[ b[ i, 1 ]b[ n-i, k-1 ], {i, 1, n-1} ];

Table[ b[ i, 4 ]/8+Sum[ b[ i, j ], {j, 5, i} ]/2+If[ OddQ[ i ], 0, 3b[ i/2, 2 ]/8

+If[ OddQ[ i/2 ], 0, b[ i/4, 1 ]/4 ]+Sum[ b[ i/2, j ], {j, 3, i/2} ]/2 ]

+Sum[ b[ j, 1 ]b[ i-2j, 2 ]/4+Sum[ If[ OddQ[ k ], b[ j,

(k-1)/2 ]b[ i-2j, 1 ], 0 ], {k, 5, i} ]/2, {j, 1, (i-1)/2} ], {i, 4, 30} ]

Cf. A000081, A036364.

Sequence in context: A119854 A037560 A138804 this_sequence A115256 A132963 A122404

Adjacent sequences: A036364 A036365 A036366 this_sequence A036368 A036369 A036370

easy,nice,nonn

Robert A. Russell (russell(AT)post.harvard.edu)